Land-based seismic data acquisition and processing techniques are used to generate a profile (image) of a geophysical structure (subsurface) of the underlying strata. This profile does not necessarily provide an accurate location for oil and gas reservoirs, but it may suggest, to those trained in the field, the presence or absence of oil and/or gas reservoirs. However the generation of this profile requires a large amount of data processing to be performed on the raw data generated by a seismic survey. Thus, providing an improved image of the subsurface in a shorter period of time via processing of the survey data is an ongoing process.
In performing seismic surveys, elastic waves are generated by the seismic survey equipment whose reflections/refractions are received by devices (geophones) that record them. Such elastic waves include primary waves (P-waves), compressional waves that are longitudinal in nature, and secondary waves (S-waves), shear waves that are transversal in nature and somewhat slower than P-waves.
The theory behind the separation of P wave data and S wave data measured by geophones has been understood for many years. In practice however, the use of this theory in applications associated with land-based seismic data acquisition has lagged far behind. Common practice in land-based seismic data acquisition is to treat the vertical (“V”) component as a proxy for the P-wave response and the horizontal (“H”) components as proxies for the S-wave response. The basis for these simplifying assumptions for multi-component processing are rooted in the observation that ray paths often arrive at the surface nearly vertically, allowing the near surface of the Earth to operate as a natural P-S wave field separation filter.
In contrast, there are several exploration contexts that have shown the H and V proxy assumption leads to the generation of unacceptable results for land-based seismic data acquisition. For example, permafrost and hard rock surfaces provide contexts where the H and V proxy assumption does not provide an accurate assessment. In fact, any location where a high velocity layer is present at the surface will lead to poor results from the H and V proxy assumption analysis.
In the referenced examples, it is common to observe, at larger offsets, the presence of P-wave energy on the horizontal components and, to a lesser extent, the presence of S-wave energy on the vertical components. It should be noted that the cross-presence of wave energy is based on the fact that under these contexts both P-wave and S-wave modes can arrive on all components. The two fundamental reasons that P-S wave field separation has not been adopted for practical applications are statics and spatial sampling.
To better understand this concept, and looking to background FIG. 1, FIG. 1(a) depicts a radiation pattern for P 102 and S 104 waves measured at the free surface for a vertical geophone and FIG. 1(b) depicts a radiation pattern for P waves, 106 and S waves, 108 measured at the free surface for a horizontal geophone. It should be noted that the free surface in these depictions is defined as the air-ground interface and the depictions are based on a paper by Dankbaar, J. W. M. (hereafter referred to simply as “Dankbaar”), entitled “Separation of P- and S-Waves”, in Geophysical Prospecting, 1985, vol. 33, pp. 970-986, the disclosure of which is incorporated herein by reference.
The complexity of the patterns illustrated in FIGS. 1a and 1b is based on solving the equations of motion in the presence of the free surface. At vertical incidence, only the P wave 102, 106 is measured on the vertical component but with double amplitude. Similarly, at horizontal incidence, only the S wave 104, 108 is measured on the horizontal component and also with double amplitude. It should be noted that the doubling of amplitude is the most obvious manifestation of the free surface effect as the upward waves are reflected by the free surface and coincide with the downward waves.
Dankbaar proposed a method to separate P waves 102, 106 and S waves 104, 108 based on the depicted patterns. The radiation patterns are functions of the slowness, i.e., “ray-parameter,” and surface P-velocities and S-velocities and can be inverted for a given slowness. The resulting operators can be applied in the F-K domain or they can also be applied in the tau-p domain after a radon transform, as described in a paper by Donati, M. S., 1997, entitled “Synthetic Example of the Benefits of P-SV AVO Analysis in the Glauconitic Channel-Blackfoot Field, Alberta,” published in the 59th EAGE Meeting, Geneva, Extended Abstracts, 2, C014 and incorporated herein by reference.
There are two fundamental assumptions implicit in the direct application of the inverse filters in the F-K domain or the tau-p domain. First, the data must be adequately and regularly sampled and second, the wave fields must be well represented as plane-waves at the surface where they are recorded. In practice, both of these assumptions can prove to be problematic. Regarding the first assumption, typical land acquisition has receivers which are well sampled in only one direction. Regarding the second assumption, the presence of statics tends to impair the representation of the wave fields as plane-waves at the surface where they are recorded. The statics problem is complicated by the fact that the separation filters depend on the slowness value at the receivers and requires performing the F-K domain or tau-p domain transform for common shot data. Satisfying the plane wave assumption would require first removing the receiver statics but this task cannot be accomplished correctly for both P and S statics until after separation.
An alternative approach is to assume that the slowness is identical at the source and the receiver and apply the separation in the receiver domain but additional problems arise with this implementation. First, the receiver gathers are more likely to be spatially aliased and second, the assumption of common slowness at the source and the receiver is only valid for a layered medium. In general, the slowness for a reflection is different on the source and receiver sides.
The problem of P-S separation in the presence of statics was previously examined by Cary, P. W., 1998, in his paper entitled “P/S wavefield separation in the presence of statics,” CREWES Research Report, Vol. 10, 30-1 to 30-8 and incorporated herein by reference and by Guevera, S. E. and Cary, P. W., 2000, in their paper entitled “A method for P-P and P-S mode separation in the presence of statics,” SEG Expanded Abstracts, 1225-1228 and incorporated herein by reference. This research proposed an adapted F-K domain/tau-p domain method in which a forward model equation describes the mapping from plane-wave data to space-time data including both statics and P-S combination and the inversion of the forward model equation. Although this model is designed to be applied in the shot domain, it assumes that statics can be determined prior to separation and that the data are well sampled spatially in the shot domain.
Accordingly, it would be desirable to provide systems and methods that avoid the afore-described problems and drawbacks, and improve the accuracy of the final image.